How to child a control point of a Bezier curve to an object
I found the solution in a YouTube video:

Suppose you want to make Object A the parent of a control point in a Bezier curve (Object B).


select Object A, then shift-select Object B (so both objects are selected)
click edit mode. Object B will open edit mode.
select the control point you want to "attach" to Object A. click ctrl+H. 
choose "selected object"


When you now move Object A, the control point will move accordingly, while the other control points of Object B won't, hence deforming the Bezier curve.

PS: you can also use this method when Object B is a simple mesh object (i.e. vertices instead of control points).